设AB两点分别为A(x1,y1) B(x2,y2)
AB满足椭圆的方程,又有
x1^2/4+y1^2=1
x2^2/4+y2^2=1
两者相减 有 (x1+x2)(x1-x2)/4+(y1+y2)(y1-y2)=0
(y1-y2)/(x1-x2)=-(x1+x2)/4(y1+y2)
又E为中点,有x1+x2=2 y1+y2=1
斜率k=(y1-y2)/(x1-x2)=-(x1+x2)/4(y1+y2)=-1/2
直线过点E,斜率已知,可以求出直线L的方程为x+2y-2=0
设AB两点分别为A(x1,y1) B(x2,y2)
AB满足椭圆的方程,又有
x1^2/4+y1^2=1
x2^2/4+y2^2=1
两者相减 有 (x1+x2)(x1-x2)/4+(y1+y2)(y1-y2)=0
(y1-y2)/(x1-x2)=-(x1+x2)/4(y1+y2)
又E为中点,有x1+x2=2 y1+y2=1
斜率k=(y1-y2)/(x1-x2)=-(x1+x2)/4(y1+y2)=-1/2
直线过点E,斜率已知,可以求出直线L的方程为x+2y-2=0